Tax bracket for SSA benefits

My husband is 65, almost 66. He started collecting SS benefits at age 62. He has 22% tax withheld from his benefits because I still work full-time and our income is in the 22% tax bracket. I am 63 years old. When I retire and start collecting SS benefits our income would then fall in the 12% tax bracket. Would I then only need to have 12% withheld from my SS for taxes? Would my husband then be able stop having 22% withheld for taxes and only need to have 12% withheld?